When it was evening, after sunset, they brought to him all who were ill or possessed by demons. The whole town was gathered at the door. He cured many who were sick with various diseases, and he drove out many demons, not permitting them to speak because they knew him.
Do demons exist? Yes. Yes, of course. Accepting that, we infer angels exist, too.
How do we know these matterless creatures exist? Well, there is the direct and massive evidence of scripture, but that true testimmony is not likely to be accepted by people not of The Book. There have also throughout history been many (let us call them) sightings and interactions. These are dismissed as being the product of overwrought minds or are called mistakes or frauds. These charges are not always false.
Since these primary sources are in dispute, can we deduce the existence of demons and angels other ways? I think so. Here is an outline of that argument originated by St Thomas, understanding that a full treatment would require a book.
We start with the true premise that our intellects and wills are not material. They are not made of stuff. We have proved this many times, and will not take the time to do so here again. We are part spirit. Since our intellects are not material, they cannot corrupt as material things do. They must continue to exist after our bodies corrupt.
Since our intellects, our rational souls if you like, exist after our bodies turn to dust, it follows that intellects without bodies can exist. And if intellects without bodies can exist, creatures which are pure spirit can exist. This follows because it is not the creation of the body that causes the intellect to exist. The body, which is made of stuff, cannot cause that which is not made of stuff to exist. Therefore there must be some other cause of spiritual substances. What this cause is we can here be agnostic about. But that it exists we cannot.
Now humans obviously choose good and choose evil, at various times. (I use evil as we have been using in our Summa Contra Gentiles tour, as the absence of the good.) We do this by will and by intellect. Since we through our spiritual selves can choose good and evil, it would seem to follow that the creatures which are pure intellects can also choose good and evil. We can call these creatures angels and demons, depending on the choices that they have made.
The nature of angels and demons are not quite like ours. They do not have bodies, as shown, and so cannot learn as we do, first of all through our senses: they have no senses to learn with. We also discovered in Summa Contra Gentiles, and elsewhere, that angels and demons learn all at once, in a flash, as it were. As do we at times: but angels and demons always. This is not exactly pertinent to proving these creatures exist, but it does show that once they come into existence, by whatever cause, their natures are fixed permanently. You cannot talk an angel who chose good into now choosing the absence of the good, and you cannot convince a demon who chose the absence of the good into now choosing the good.
Why is that important? Because, of course, these creatures can interact with us because we are partly spiritual creatures. And do interact with us. You can have “intellectual discussions”, to stretch a term, with them. (I for many years willingly had the wrong conversations.) They cannot in general be seen or heard to have these conversations, because they possess nothing material to be seen or heard. But it does not follow that they can never be seen or heard; or rather, it does not follow that their effects can never be seen or heard. Here’s why.
Somehow our spiritual natures interact with our physical selves. How? I haven’t the slightest idea. I am like the caveman transported to an airport asked how these massive chunks of steel can lift themselves into the sky. I cannot say why it happens; I only know that it does. It should be obvious that because I do not know how is in no way proof that airplanes cannot fly.
I do not accept Descartes’s ghost in the machine, of course, but do insist on our partly non-material natures. Accepting this, it then follows that spirits can influence material things somehow. Thus it follows angels and demons can sometimes be “seen” and “heard’ when influencing material things. What are the extent of their powers to influence material things? Again, I do not know. It is not something that can be proven from first principles, like existence can, but has to be inferred from experience.
Experience can be used, too, because since we have proven the existence of demons and angels, and have inferred that they have the potential to influence material things, there is no difficulty accepting the potential of eyewitness reports. And if we can accept, on principle, the veracity of some eyewitness reports, we can accept the most reliable of eyewitness reports in scripture.
We must also accept that human-demon-angel interactions happen not in the distant “pre-scientific” past, but in the here-and-now. To you.